Quasi Binary

Description:

Input:

The first line contains a single integer n (1 ≤ n ≤ 10⁶).

Output:

In the first line print a single integer k — the minimum number of numbers in the representation of number n as a sum of quasibinary numbers.

In the second line print k numbers — the elements of the sum. All these numbers should be quasibinary according to the definition above, their sum should equal n. Do not have to print the leading zeroes in the numbers. The order of numbers doesn't matter. If there are multiple possible representations, you are allowed to print any of them.

Sample Input:

9

Sample Output:

9
1 1 1 1 1 1 1 1 1 

Sample Input:

32

Sample Output:

3
10 11 11